Classification of c=1 CFTs
Lorenz Eberhardt, Nat Levine
Abstract
We completely classify unitary 2d CFTs with central charge c=1 and discrete spectrum. We confirm the folklore that the only such theories are the compact free boson, its Z2-orbifold, and three exceptional theories obtained as orbifolds of the SU(2)1 WZW model. The proof is by recasting the c=1 modular bootstrap as a crystalline measure problem for the density of states, and analytically solving it. We also show that, once the density of states is specified, the full CFT can be uniquely reconstructed.
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